| The goal of this research is to develop efficient and robust model reduction methods, which are applied to reduce the DOF of large complex finite element models for structural dynamics and vibration analyses, in both low-frequency and banded, mid-frequency ranges. The current study extends significantly the application and utility of the quasi-static compensation (QSC) methodology.; Modal superposition, Ritz vector and component mode synthesis techniques have been employed widely as model reduction methods. All these approaches have some restrictions that limit their use for dynamics problems associated with wide or bounded frequency ranges of interest, e.g., a large number of generalized coordinates may be required to expand the desired configuration space, which significantly reduces the methods' efficiency. These limitations have prevented overall acceptance and use of the standard reduction methods by practicing engineers.; In this dissertation, the concept of quasi-static compensation, as an efficient model reduction tool, has been utilized and extended to develop new techniques of reducing problem size in the generalized coordinate domain, using the load dependent Ritz vector method, component mode synthesis, and dynamic data recovery. The proposed methods are well suited for a broader class of structural dynamics problems, including harmonic frequency response analysis, transient response analysis, and coupled structural-acoustic analysis.; The new model reduction methods exhibit substantial improvements compared with existing techniques. Applicable to a broader class of problems, their performance is ideal for banded, mid-frequency dynamics analyses. Specifically, the new quasi-static Ritz vector (QSRV) algorithm is more efficient, accurate, and stable, with respect to recurrence orthogonality; the new quasi-static mode (QSM) approach combines the computational efficiency of standard component mode synthesis with higher accuracy, and further efficiency is gained by only retaining the component normal modes in the frequency range of interest; the new quasi-static mode acceleration (QSMA) method compensates for both truncated lower- and higher-frequency modes in modal solutions, and improved recovery accuracy can be achieved.; A variety of academic and industrial strength problems are presented to illustrate the enhanced efficacy of the new methodologies. Discussions concerning these model reduction methods and general guidelines for use are also provided. |
